Transcription

2 The Electric Field Replaces action-at-a-distance Instead of Q 1 exerting a force directly on Q at a distance, we say: Q 1 creates a field exerts a force on Q. and then the field NOTE: Since force is a vector then the electric field must be a vector field! E F qe

3 Does the field really exist? It exists due to the finite speed of light (maximum speed of signal propagation) Electric charges in isolating shells Isolation removed (door open) Force is exerted after the source charge is isolated Interaction by the field rather than by charge

4 Field E is defined as the force that would be felt by a unit positive test charge E F / q 0 SI units for the electric field: newtons per coulomb.

5 Electric Field Lines We visualize the field by drawing field lines. These are defined by three properties: Lines point in the same direction as the field. Density of lines gives the magnitude of the field. Lines begin on + charges; end on charges.

6 Electric field created by a negatively charged metal sphere

7

8

9 Coulomb s Law for the Field Coulomb s law for the force on q due to Q: F k qq r rˆ qe Coulomb s law for the field E due to Q: E k Q r rˆ

10 Example 1 What is the electric field strength at a distance of 10 cm from a charge of μc? E kq r ( )( 10 (10 10 ) 6 ) N / C So a one-coulomb charge placed there would feel a force of 180,000 newtons.

11 Q.-1 A point charge Q is far from all other charges. At a distance of m from Q, the electric field is 0 N/C. What is the electric field at a distance of 4m from Q? 1. 5 N/C. 10 N/C 3. 0 N/C N/C N/C

14 The shell theorems for E In Chapter 13 we had the shell theorems for gravity In Chapter 1 (p. 567) the shell theorems for electrostatics were stated. In Chapter 3 (p. 618) they will be proven. But we can easily understand them now from our knowledge of electric field lines.

15 The shell theorems for gravity Given a uniform spherical shell of mass: (1) The field outside is the same as if all the mass were concentrated at the center. () The field inside the shell is zero. (These theorems for gravity are given in Chapter 14.) (Newton s headache!)

16 Prove true also for electric field Use our knowledge of electric field lines to draw the field due to a spherical shell of charge: There is no other way to draw lines which satisfy all 3 properties of electric field lines, and are also spherically symmetric. Notice that both shell theorems are obviously satisfied.

18 Useful result for spherical r symmetry Field outside a sphere of total charge Q is radially outward with magnitude E kq r

19 Q.- A shell of uniform charge attracts or repels a charged particle that is outside the shell as if all the shell s charge were Concentrated at the center.. Concentrated at the point closest to the particle. 3. Concentrated at the point opposite the particle. 4. Zero.

20 Electric Dipole The combination of two charges of equal but opposite sign is called a dipole. If the charges +q and q are separated by a distance d, then the dipole moment p is defined as a vector pointing from q to +q of magnitude p = qd. q p q

21 Electric Field Due to a Dipole

22 Torque on a Dipole in a Field d F ( sin ) qe d sin pe p E sin

23 Chapters, 3: The Electric Field NOTE! If you have urgent questions, please send me e- mail with Your name Section At

25 Electric Field Lines We visualize the field by drawing field lines. These are defined by three properties: Lines point in the same direction as the field. Density of lines gives the magnitude of the field. Lines begin on + charges; end on charges. From these properties it is easy to see that Field lines never cross

26 Coulomb s Law for the Field Coulomb s law for the force on q due to Q: F k qq r rˆ qe Coulomb s law for the field E due to Q: E k Q r rˆ

28 Q.-1 What is the SI unit for the electric field? 1. Newtons. Coulombs 3. Newtons per Coulomb 4. Newtons per meter 5. Coulombs per meter

29 Q.-1 What is the SI unit for the electric field? Field is force per unit charge: 1. Newtons. Coulombs 3. Newtons per Coulomb 4. Newtons per meter 5. Coulombs per meter F qe

30 Three charges (one + and two -) are placed on the x and y axes as shown. What is the approximate direction of the electric field at the origin? Will it be pointing toward point 1,, 3, or 4? E Q.- -q 1 3 +q -q 4

31 Q.- 1. (1). () 3. (3) 4. (4) -q 1 3 +q -q 4

32 Q.- Three charges (one + and two -) are placed on the x and y axes as shown. What is the approximate direction of the electric field at the origin? Will it be pointing toward point 1,, 3, or 4? Solution. Imagine a positive test charge placed at the origin. It will be atracted to the q charges and repelled by the +q charge. 3 +q -q E 1 -q 4

33 Linear charge distribution Linear charge density = charge per unit length If a rod of length.5 m has a uniform linear charge density λ = 3 C/m, then the total charge on the rod is (.5 m) (3 C/m) = 7.5 C. If a rod of length L carries a non-uniform linear charge density λ(x), then adding up all the charge produces an integral: b Q ( x) dq a b a dx

38 Charged ring result E k cos dq Q k cos r r kqz 3 r kqz ) ( z R 3/ NOTE: This is a good example of a special result, which is the answer to an example problem, not a fundamental principle to be memorized. It is the process we are supposed to be learning, not the result!

39 NOTE This result for the field on the axis of a charged ring can be derived more easily in Chapter 4 using the idea of electric potential.

40 Electric Dipole The combination of two charges of equal but opposite sign is called a dipole. If the charges +q and q are separated by a distance d, then the dipole moment p is defined as a vector pointing from q to +q of magnitude p = qd. q p q

41 Electric Field Due to a Dipole

42 Torque on a Dipole in a Field d F ( sin ) qe d sin pe p E sin

43 Gauss s Law Gauss s Law is the first of the four Maxwell Equations which summarize all of electromagnetic theory. Gauss s Law gives us an alternative to Coulomb s Law for calculating the electric field due to a given distribution of charges.

44 Gauss s Law: The General Idea The net number of electric field lines which leave any volume of space is proportional to the net electric charge in that volume. E lines leaving V volume V E lines entering V

45 Flux The flux Φ of the field E through the surface S is defined as E da S The meaning of flux is just the number of field lines passing through the surface.

46 Best Statement of Gauss s Law The outward flux of the electric field through any closed surface equals the net enclosed charge divided by ε 0.

47 Gauss s Law: The Equation S E da Q / enc 0 S is any closed surface. Q enc is the net charge enclosed within S. da is an element of area on the surface of S. da is in the direction of the outward normal SI units

22.1 ntroduction We have seen in chapter 21 that determining the electric field of a continuous charge distribution can become very complicated for some charge distributions. t would be desirable if we

CHAPTER 4 GAUSS S LAW 4. The net charge shown in Fig. 4-40 is Q. Identify each of the charges A, B, C shown. A B C FIGURE 4-40 4. From the direction of the lines of force (away from positive and toward

[ Assignment View ] [ Eðlisfræði 2, vor 2007 22. Gauss' Law Assignment is due at 2:00am on Wednesday, January 31, 2007 Credit for problems submitted late will decrease to 0% after the deadline has passed.

1. Which diagram represents the electric field lines between two small electrically charged spheres? 2. Which graph best represents the relationship between the magnitude of the electric field strength,

INTRODUCTION We will understand how electric and magnetic fields affect charged particles Lorentz Force Law: we will learn to describe how electric and magnetic fields are produced by charged particles

Gauss s Law for Gravity D.G. impson, Ph.D. Department of Physical ciences and Engineering Prince George s Community College December 6, 2006 Newton s Law of Gravity Newton s law of gravity gives the force

ELECTROSTATICS One Marks Questions with Answers: 1.What is an electric charge? Ans: It is a fundamental property of matter which is responsible for all electrical effects 2. Write the SI unit of charge?

Coefficient of Potential and Capacitance Lecture 12: Electromagnetic Theory Professor D. K. Ghosh, Physics Department, I.I.T., Bombay We know that inside a conductor there is no electric field and that

Chapter 25: Capacitance Most of the fundamental ideas of science are essentially simple, and may, as a rule, be expressed in a language comprehensible to everyone. Albert Einstein 25.1 Introduction Whenever

4. A 2-g ping-pong ball rubbed against a wool jacket acquires a net positive charge of 1 µc. Estimate the fraction of the ball s electrons that have been removed. If half the ball s mass is protons, their

Phy 49 Fall 11 Solutions 1. Three charges form an equilateral triangle of side length d = 1 cm. The top charge is q = - 4 μc, while the bottom two are q1 = q = +1 μc. What is the magnitude of the net force

III. ELECTRICITY AND MAGNETISM A. Electrostatics 1. Charge and Coulomb s Law a) Students should understand the concept of electric charge, so they can: (1) Describe the types of charge and the attraction

CHAPTER 6 ELECTROSTATIC ENERGY AND CAPACITORS. Three point charges, each of +q, are moved from infinity to the vertices of an equilateral triangle of side l. How much work is required? The sentence preceding

Chapter 27 Solutions PSS 27.2 The Electric Field of a Continuous Distribution of Charge Description: Knight Problem-Solving Strategy 27.2 The Electric Field of a Continuous Distribution of Charge is illustrated.

. The Electric Field Concepts and Principles Electric Charge, Electric Field and a Goofy Analogy We all know that electrons and protons have electric charge. But what is electric charge and what does it

Three point charges are located at the corners of a right triangle as shown, where q 1 = q 2 = 3 µc and q 3 = -4 µc. If q 1 and q 2 are each 1 cm from q 3, what is the magnitude of the net force on q 3?

Physics 9 Fall 009 Homework - s 1. Chapter 7 - Exercise 5. An electric dipole is formed from ±1.0 nc charges spread.0 mm apart. The dipole is at the origin, oriented along the y axis. What is the electric

PHY2049 Summer 2012 Instructor: Francisco Rojas Exam 1 As customary, choice (a) is the correct answer in all the following problems. Problem 1 A uniformly charge (thin) non-conucting ro is locate on the

Chapter 27 Magnetic Field and Magnetic Forces - Magnetism - Magnetic Field - Magnetic Field Lines and Magnetic Flux - Motion of Charged Particles in a Magnetic Field - Applications of Motion of Charged

Chapter 13 Gravitation 13.2 Newton s Law of Gravitation In vector notation: Here m 1 and m 2 are the masses of the particles, r is the distance between them, and G is the gravitational constant. G = 6.67

Ch 9 Rotation 9.1 Rotational Kinematics: Angular Velocity and Angular Acceleration Q: What is angular velocity? Angular speed? What symbols are used to denote each? What units are used? Q: What is linear

I wish to give an account of some investigations which have led to the conclusion that the carriers of negative electricity are bodies, which I have called corpuscles, having a mass very much smaller than

Chapter 5. Magnetostatics and Electromagnetic Induction 5.1 Magnetic Field of Steady Currents The Lorentz force law The magnetic force in a charge q, moving with velocity v in a magnetic field B in a magnetic

If two identical balls each of mass m and having charge q are suspended by silk thread of length l from the same point o,then the distance between the balls is given by : = X = 2 ( ) 1 Two pith balls each

Lab 4. Magnetic Fields Goals To visualize the magnetic fields produced by several different configurations of simple bar magnets using iron filings. To use small magnetic compasses to trace out the magnetic

Give the equation relating to the force between point charges in a vacuum If 'F' (the force) is negative what does that mean? If 'F' (the force) is positive what does that mean? State Coulomb's Law F is

Magnetic vector potential When we derived the scalar electric potential we started with the relation r E = 0 to conclude that E could be written as the gradient of a scalar potential. That won t work for

Physics 201 Homework 8 Feb 27, 2013 1. A ceiling fan is turned on and a net torque of 1.8 N-m is applied to the blades. 8.2 rad/s 2 The blades have a total moment of inertia of 0.22 kg-m 2. What is the

Magnetostatics II Lecture 4: Electromagnetic Theory Professor D. K. Ghosh, Physics Department, I.I.T., Bombay Magnetic field due to a solenoid and a toroid A solenoid is essentially a long current loop

Chapter The Stern-Gerlach Experiment Let us now talk about a particular property of an atom, called its magnetic dipole moment. It is simplest to first recall what an electric dipole moment is. Consider

Forces between charges Two small objects each with a net charge of Q (where Q is a positive number) exert a force of magnitude F on each other. We replace one of the objects with another whose net charge

Chapter 1 1.1 What must the distance between point charge 6 10 6 C and point charge q 47 10 6 C for the electrostatic force between them to be 5.70N? The magnitude of the force of attraction is given by

TOPIC 1 ELECTROSTTICS PHY11 Electricity an Magnetism I Course Summary Coulomb s Law The magnitue of the force between two point charges is irectly proportional to the prouct of the charges an inversely

11. Rotation Translational Motion: Motion of the center of mass of an object from one position to another. All the motion discussed so far belongs to this category, except uniform circular motion. Rotational

Name Date(YY/MM/DD) / / St.No. - Section UNIT 102-1: ELECTRIC FORCES AND FIELDS Electricity is a quality universally expanded in all the matter we know, and which influences the mechanism of the universe

University of California, Berkeley Physics H7B Spring 1999 (Strovink) SOLUTION TO PROBLEM SET 5 Solutions by P. Pebler 1 Purcell 1.16 A sphere of radius a was filled with positive charge of uniform density

Chapter 14: Magnets and Electromagnetism 1. Electrons flow around a circular wire loop in a horizontal plane, in a direction that is clockwise when viewed from above. This causes a magnetic field. Inside

Physics 1A Lecture 10C "If you neglect to recharge a battery, it dies. And if you run full speed ahead without stopping for water, you lose momentum to finish the race. --Oprah Winfrey Static Equilibrium

P HYSICS 301: I NTERMEDIATE E LECTROMAGNETISM 1. Short Answer 30 points total FALL 2010, A SSESSMENT #3 (F INAL ) None of the problems in this section should require an involved calculation or a complicated

MOVING CHARGES AND MAGNETISM 1. A circular Coil of 50 turns and radius 0.2m carries of current of 12A Find (a). magnetic field at the centre of the coil and (b) magnetic moment associated with it. 3 scores

The moon is essentially gray, no color. It looks like plaster of Paris, like dirty beach sand with lots of footprints in it. -James A. Lovell (from the Apollo 13 mission) David J. Starling Penn State Hazleton

Chapter 1 Gauss Formulation of the gravitational forces 1.1 ome theoretical background We have seen in class the Newton s formulation of the gravitational law. Often it is interesting to describe a conservative